A grinding plant with two-stage classification is known in the art in which the brittle material for grinding is first of all crushed in a primary mill, particularly a material bed roller mill with two rollers pressed against one another with high pressure, and is delivered to a first classifier. There the crushed material for grinding is classified into a coatset and a finer fraction. Whilst the coatset fraction is returned to the primary mill the finer fraction is conveyed pneumatically into a second classifier arranged overhead. The classification into coarse and fine material takes place there. The coarse material is then ground in a fine grinding mill, particularly a ball mill, and from there is fed into the vertical uptake pipe between the first and second classifiers. From there the material ground in the fine grinding mill is pneumatically conveyed together with the finer fraction from the first classifier into the second classifier. However, the pneumatic conveying of the material to be classified is unfavourable in energy terms.